How do you differentiate #g(x) = (x^2+1) (x^2-3x)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Jothi S. Jan 4, 2016 #g'(x)=4x^3-6x^2+2x-2# Explanation: #g(x)=(x^2+1)(x^2-2x)# Product rule :#d/dx(uv)=(du)/dxv+u(dv)/dx# #u=(x^2+1)# #du/dx=2x# #v=x^2-2x# #dv/dx=2x=2# #d/dx(x^2+1)(x^2-2x)=(du)/dxv+u(du)/dx# =#2x(x^2-2x)+(x^2+1)(2x-2)# =#2x^3-4x^2+2x^3-2x^2+2x-2# =#4x^3-6x^2+2x-2# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 1465 views around the world You can reuse this answer Creative Commons License